In rising from the bottom of a lake to the top, the temperature of an air bubble remains unchanged, but its diameter is doubled. If h is the barometric height (expressed in metres of mercury of relati

Question

In rising from the bottom of a lake to the top, the temperature of an air bubble remains unchanged, but its diameter is doubled. If h is the barometric height (expressed in metres of mercury of relative density ρ ) at the surface of the lake, the depth of the lake is (in metres):

TestHub · Accepted Answer

The volume rises 8 times, so P b o tt o m ​ = 8 P 0 ​ . The extra pressure 7 P 0 ​ is that of the water column. P 0 ​ = ρ h metres of water, so depth = 7 ρ h . C.

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